Water Resources Research

A geochemical transport model for thermo-hydro-chemical (THC) coupled processes with saline water

Authors


Abstract

[1] Anhydrous MgSO4 is considered as a potential sealing material for the isolation of high-level-waste repositories in salt rock. When an aqueous solution, usually a brine type, penetrates the sealing, different MgSO4 hydrates along with other mineral phases form, removing free water from the solution. The uptake of water leads to an overall increase of solid phase volume. If deformation is constrained, the pore volume decreases and permeability is reduced. In order to simulate such processes, especially for conditions without free water, a coupling between OpenGeoSys and thermodynamic equilibrium calculations were implemented on the basis of the commercially available thermodynamic simulator ChemApp and the object-oriented programming finite-element method simulator OpenGeoSys. ChemApp uses the Gibbs energy minimization approach for the geochemical reaction simulation. Based on this method, the thermodynamic equilibrium of geochemical reactions can be calculated by giving the amount of each system component and the molar Gibbs energy of formation for all the possible phases and phase constituents. Activity coefficients in high-saline solutions were calculated using the Pitzer formalism. This model has the potential to handle 1-D, 2-D, and 3-D saturated and nonsaturated thermo-hydro-chemical coupled processes even with highly saline solutions under complex conditions. The model was verified by numerical comparison with other simulators and applied for the modeling of SVV experimental data.

1. Introduction

[2] In Germany rock salt is considered as the potential host rock for a high-level-waste (HLW) repository owing to its favorable properties, such as low permeability, plasticity, and extremely dry conditions in general. The most probable evolution of a repository in rock salt is that there will be no contact between waste and aqueous solution at all.

[3] In the improbable event that aqueous solution does enter into the vicinity of the waste, precautions have to be made to slow down water movement at a rate that keeps exposure to radiation of the biosphere below certain threshold values. One such measure is the filling of boreholes between the HLW canister and the host rock with anhydrous MgSO4 [Delfs et al., 2010], often referred to as SVV (the German abbreviation for Selbst Verheilender Versatz, meaning self-sealing backfill). SVV is considered as a potential backfill or engineered barrier material for such purpose. When brine enters the barrier, SVV reacts with free water in the brine and forms different MgSO4 hydrates along with other phases. The total volume of the solid phases therefore increases and the pore space decreases. Consequently, the permeability of the SVV is reduced. If deformation is constrained, crystal pressure is built up, which can be measured in the laboratory. Such complex processes can be better understood with the aid of reactive transport simulation.

[4] Considerable progress has been made in the past decade in modeling reactive transport in nature systems [Lichtner, 1985, 1988; Ortoleva et al., 1987; Liu and Narasimhan, 1989; Nienhuis et al., 1991; Yeh and Tripathi, 1991; Simunek and Suares, 1994; Steefel and Lasaga, 1994; Steefel and MacQuarrie, 1996; Parkhurst and Appelo, 1999; Xu and Pruess, 2001; Mayer et al., 2002; Xie et al., 2006, 2007; Shao et al., 2009]. Two approaches have been used for the calculation of chemical reactions. In both approaches a global thermodynamic equilibrium is calculated. The first one is based on the law of mass action (limited area model (LAM) method), which is most commonly used in the current reactive transport simulators. This approach solves the root of a system of a set of nonlinear algebraic equations representing the whole geochemical system at equilibrium. The geochemical programs PHREEQC [Parkhurst and Appelo, 1999], PHT3D [Prommer, 2002], and EQ3/6 [Wolery, 1992] are all based on this approach. EQ3/6 was employed to simulate benchmarks for comparison. The second approach is the Gibbs energy minimization (GEM) method. This approach minimizes the total Gibbs energy of the system by distributing the system components along all possible phases and phase constituents. The programs GEM-Selektor [Karpov et al., 2001] and CHEMAPP [Eriksson et al., 1997] also follow this approach. Theoretically, both methods should provide the same results for the same problem. It is important to note that all codes based on the LAM method encounter problems under extremely dry or no water conditions, which is the case for the SVV experiment. Similar conditions can also occur in geothermal reservoirs and during CO2 sequestration. Such environments also feature high temperature, high salinity, and high pressure [Zhang et al., 2005; Regenspurg et al., 2010].

[5] This paper provides a new reactive transport model that has been developed based on the GEM method for geochemical equilibrium reactions. The object-oriented finite-element method (FEM) simulator OpenGeoSys [Wang et al., 2009] is coupled with the thermodynamic simulator ChemApp. ChemApp has been widely applied to the analysis of chemical processes in industrial applications, e.g., in the steel, cement, and chemical industry, under high pressure, high temperature, and high salinity, or even nonaqueous conditions.

2. Theoretical Background

[6] The new reactive transport model has been developed for fully saturated porous media where the aqueous and/or gaseous phases are considered mobile, while the solid phases are considered immobile. The general equations for liquid flow and mass transport can be found in the work of Kolditz [1995] and Bear [1988].

2.1. Gibbs Energy Minimization

[7] Conceptually, any system consists of one or more phases, each of which contains constituents, which in turn are built up from system components. System components are the smallest entities any system is composed of. In the simplest case system components are identical with chemical elements, which form aqueous species (constituents of the aqueous phase), gaseous species (constituents of the gas phase), or solid phases. However, depending on the system under consideration, system components can also represent aqueous species or solids, which can render the numerical problem easier to solve.

[8] The Gibbs energy minimization approach uses mass balance as a constraint and allocates system components to constituents of all possible phases such that the Gibbs energy of the system is minimized

equation image
equation image

in which GT,p is the total Gibbs energy of the defined system at given temperature (T) and pressure (p), NP is the number of phases, NC is the number of constituents for each phase, ni,j is the amount of the jth constituent in the ith phase, and equation image is the molar Gibbs energy of formation for the jth constituent in the ith phase.

[9] The minimization of the Gibbs energy can be performed by different mathematical approaches [Smith and Missen, 1991]. It is widely used for simulating equilibrium chemical reactions. However, it can also be applied to model kinetic-controlled reactions [Koukkari and Pajarre, 2006], which are not included in the current work owing to the fact that the chemical reactions for the SVV experiment were relatively fast. For the subject of interest one can assume that all precipitation and dissolution reactions in the SVV sealing are proceeding at a rate high enough to justify neglection of reaction kinetics.

[10] ChemApp is a programmer's library based on the Gibbs energy minimization technique developed by Eriksson et al. [1997]. It consists of a rich set of subroutines, which provides almost all the necessary tools for the calculation of complex multicomponent, multiphase chemical equilibria, and the determination of the associated energy balances, such as different Pitzer equations [GTT-Technologies, 2006].

[11] Physical parameters such as the density of all phases (i.e., gas, liquid, and solid) and porosity are changing with the reactive transport process owing to the compositional variation of the chemical constituents or minerals. These can be handled with ChemApp. The essential step for calculating density values of each phase is to compute the total volume of each phase. For gas, it was normally derived by the idea gas law. The total volume of the aqueous or solid phase is derived by

equation image

in which VT,p is the total volume of the aqueous or solid phase (exclusive pore volume) at given temperature (T) and pressure (p); Vi is the partial molar volume for the chemical component i in the aqueous phase, and the molar volume for the solid phase i, respectively. The porosity can be computed using

equation image

in which Vtot is the total volume (inclusive pore volume).

[12] Different database formats are possible for ChemApp. For this work we set up a database which contained the Gibbs energy of formation for each chemical species in aqueous solutions and for each solid mineral. Additional parameters may be required for other purposes. In the present case, Pitzer parameters had to be added for simulating highly concentrated aqueous solutions, as well as solid phase molar volumes, and partial molar volumes for aqueous species.

2.2. Coupling Scheme

[13] The object-oriented program OpenGeoSys was adopted to solve the system of coupled processes. The coupling processes are schematically described in Figure 1. Time is discretized using Euler time steps and spatial discretization by the finite element method. For each time step, fluid flow and heat transport are calculated. Because these two processes are strongly coupled via material properties, the program iterates between them [Kolditz and de Jonge, 2004]. Reactive mass transport is separated using an operator splitting technique and a two-step noniterative sequential approach. In the first step, conservative transport is calculated for all chemical components based on the phase velocities calculated for flow, while in the second step the geochemical reactions are simulated. In this work, transport and reactions are calculated only in the liquid phase. For the reaction step, the geochemical simulator ChemApp [Eriksson et al., 1997] is employed. The OpenGeoSys simulator is designed using object-oriented and process-oriented methods, which allows the coupling of liquid flow, heat transport, mass transport, chemical reactions, and deformation in an efficient way [Wang et al., 2006].

Figure 1.

Schematic representation of the coupling concept used in OpenGeoSys. The objects are FFC, fluid flow; HTM, heat transport; MTM, multicomponent mass transport; ERM, chemical reaction.

3. Numerical Method

[14] The Galerkin finite-element method was applied to solve the weak forms of all the governing equations described above in this section. Owing to the fact that similar types of partial differential equations (PDEs) for diverse physical problems differ only in material coefficients, element class and objects were developed by Wang and Kolditz [2007] and applied to deal with the local element matrices and vectors arising from the finite element discretization of the PDEs. These element functions are thus able to deal with different element types (lines, triangles, quadrilaterals, tetrahedra, prims, hexahedra) by automatically choosing the related element interpolation functions. Therefore, the new reactive transport model can be used for 1-D, 2-D, and 3-D problems.

4. Benchmarks

4.1. Reactive Transport Coupling

[15] A 1-D transport and calcite dissolution case was adopted to verify the coupling. This test example was proposed by Engesgaard and Kipp [1992] for a model verification of their MST1D code against the CHEMTRNS model by Noorishad et al. [1987]. It was later used by Prommer [2002] to verify PHT3D. The one-dimensional model domain was 0.5 m long and composed of porous media with porosity of 0.32 and bulk density of 1800 kg/m3. The pore water was initially in equilibrium with calcite (2.176 × 10−5mol/kg soil). This sample was successively flushed with 0.001 M MgCl2 solution from one end (Figure 2), leading to multiple precipitation/dissolution fronts. Dolomite was not present initially but formed temporally (Figure 3). The thermodynamic database used is based on the NAGRA/PSI database [Hummel et al., 2002].

Figure 2.

Comparison of simulated ionic concentrations and pH.

Figure 3.

Comparison of simulated minerals (a) calcite and (b) dolomite.

4.2. Geochemical Reaction Simulations

[16] To demonstrate the operational reliability of ChemApp for geochemical reaction simulation, the following examples are presented: (1) rock salt dissolution and (2) adding SVV to saturated NaCl solution. The simulated results were compared with the results simulated with EQ3/6.

[17] Thermodynamic equilibrium between mineral phases and aqueous solution in the system NaCl-MgSO4-H2O was calculated applying the Pitzer model [Pitzer, 1973, 1975, 1991; Pitzer and Kim, 1974]. The database data0.hmw provided by EQ3/6 was used for rock salt dissolution calculated with EQ3/6; while the database data0.ypf (Yucca Mountain Pitzer File) provided by EQ3/6 was used for the other EQ3/6 calculations. The databases were transformed into a ChemApp format for corresponding ChemApp calculations.

[18] Data as given in data0.hmw were published by Harvie et al. [1984]. The development of Pitzer parameters and solubility constants for temperatures higher than 25.0°C as given in data0.ypf is documented in Mariner [2005]. Those data are suitable for calculations for temperatures up to 300°C, depending on the system considered. With the data given in the two parameter files thermodynamic equilibria can be calculated for arbitrary system compositions in terms of Na+, Cl, K+, Mg2+, SO42−, and H2O. The density of solution and specific volumes of all mineral phases were evaluated. The presented test case was calculated for room temperature 25°C only.

4.2.1. Rock Salt Dissolution

[19] Upon solution mining, saturated or nearly saturated NaCl-solution is created which must not be disposed of in surface discharge systems. Instead, it was considered (and, in fact, put into practice) to pump those solutions into abandoned salt mines. Prior to such activities one was interested in the possible reactions taking place, especially the question, how much volume of host rock was going to be dissolved? This process was thoroughly investigated by Herbert [2000].

[20] The mineral composition of the rock salt is shown in Table 1. About 16.0 kg rock salt was gradually added to a pool of saturated NaCl solution with 1 kg H2O. The related geochemical processes were simulated with ChemApp and EQ3/6. By utilizing both simulators, the results were almost identical as demonstrated in Figures 4 and 5. At the beginning, KMgCl3 × 6H2O (carnallite) and MgSO4 × H2O (kieserite), both containing crystal water, were dissolved (Figure 4). This resulted in an increase in the amount of H2O in the solution (Figure 4). The concentration of all ions except Na+ increased. With further addition of rock salt, a new mineral, K2MgSO4 × 4H2O (leonite), was formed and increased up to 1.9 mol and dissolved when another new mineral, KMgClSO4 × 3H2O (kainite), formed followed by carnallite saturation. With the precipitation of carnallite and kainite, free water was removed from the solution. Finally, no free water was left when the added rock salt amounted to 15.4 kg. It is interesting to note that ChemApp could give a reasonable mineral composition even when there was no aqueous phase left in the system as shown in Figure 4, while the EQ3/6 calculation was terminated when the amount of H2O decreased to a very small amount.

Figure 4.

Reaction of rock salt with saturated NaCl-solution: amount of free water and solid phases as calculated with ChemApp (symbol) and EQ3/6 (line).

Figure 5.

Reaction of rock salt with saturated NaCl-solution: solute concentrations as calculated with ChemApp (symbol) and EQ3/6 (line).

Table 1. Mineral Composition of Rock Salta
MineralChemical FormulaMass (%)Content (mol/kg)
HaliteNaCl508.5555
SylviteKCl182.4145
KieseriteMgSO4:H2O251.8066
CarnalliteKMgCl3:6H2O70.2519

4.2.2. Adding SVV to Saturated NaCl Solution

[21] SVV is composed of anhydrous MgSO4 and reacts with water very quickly and exothermally. All possible minerals for SVV with saturated NaCl solution are listed in Table 2. To simulate the geochemical processes during the addition of SVV to saturated NaCl solution containing 1 kg water, equilibrium calculations with both EQ3/6 and ChemApp were undertaken. The comparison of the simulated results matched very well (Figures 6 and 7). Upon the addition of SVV to the solution, Na2Mg(SO4)2 × 4H2O (bloedite) precipitates. Consequently, the amount of free water decreases. Because the initial solution is already saturated with respect to NaCl (halite), halite precipitates along with bloedite. The total volume of all solid phases increases. The volume of bloedite reaches its maximum with about 4 mol of SVV added. With the further addition of SVV, bloedite begins to dissolve and epsomite is formed. The amount of free water decreases quickly until it disappears. The correspondent ionic concentrations (in mol/kg × H2O) also change with the addition of SVV and remain constant when more than 4 mol SVV are added (Figure 7).

Figure 6.

Reaction of saturated NaCl-solution with SVV: comparison of solid phase volumes and amount of free water calculated with ChemApp and EQ3/6.

Figure 7.

Reaction of saturated NaCl-solution with SVV: Comparison of solute concentrations calculated with ChemApp and EQ3/6.

Table 2. Molar Volume and Standard Molar Gibbs Energy of Formation of Mineralsa
MineralChemical FormulaeMolar volume (cm3/mol)equation image (J/mol)
  • a

    Standard Molar Gibbs energy of formation is equation image.

HaliteNaCl27.02−8.75 × 105
ThenarditeNa2SO453.33−3.81 × 106
BloediteNa2Mg(SO4)2×4H2O149.98−3.43 × 106
MgSO4MgSO445.25−3.46 × 106
KieseriteMgSO4 × H2O56.60−3.73 × 106
StarkeyiteMgSO4 × 4H2O95.74−4.47 × 106
PentahydriteMgSO4 × 5H2O110.76−4.72 × 106
HexahydriteMgSO4 × 6H2O132.58−4.96 × 106
EpsomiteMgSO4 × 7H2O146.80−5.20 × 106

5. Application

[22] A 2-D test example was based on a laboratory experiment to demonstrate the capability of the model for simulating reactive transport process in the case of high saline solution, or even no water conditions.

5.1. Experiment

[23] To isolate hazardous waste in salt rock formations a sealing material is needed which is geochemically stable on a long-term timescale and reacts to form a low-permeable barrier upon contact with aqueous solution. Ideally, the end state of this material has the same or similar mechanical properties as the surrounding rock salt.

[24] SVV consists of anhydrous MgSO4 powder with a grain size less than 2 mm (in which more than 90% is in the fraction between 0.25 and 1.0 mm). The grain density is 2660 kg/m3. Upon contact with aqueous solution, SVV can react in a very short time period and form a hard and low-permeable solid material with similar mechanical properties to rock salt. Additionally, the total volume of solid phases increases and results in crystallization pressure. To study this, granular anhydrous MgSO4 was placed inside a cylindrically shaped rigid containment with a height of 0.14 m and a radius of 0.07 m. The sample was compacted but remained very porous with a porosity of 50.2%. The initial gas permeability was 3.02 × 10−10 m2. Saturated NaCl-solution was percolated through the sample from the bottom to the top. The liquid pressure (injection), the injection flowrate, and the total pressure inside the sample were recorded (Figure 8). Owing to the relatively high permeability, saline solution entered the sample easily at the beginning (Figure 8a). The flux was as high as about 5.0g/(sec × m2). After 1.6 h, the flowrate slowed down dramatically. To maintain the flux rate, injection pressure was increased up to 3.5 MPa. However, this method failed after only 0.3 h. The flux dropped suddenly and remained constant as low as 0.2g/(sec × m2), and an additional 2 h later to 0.05 g/(sec × m2). The total pressure measured reached the peak value at 5.95 MPa after 7 h from the beginning of the experiment. After 2 days almost no more solution could be injected into the sample. At that time, the flow system was closed. On the twentieth day the sample was reopened to the injection system with the pressure at 3.5 MPa. No solution could be injected into the sample. One week later, the injection pressure was removed. However, the recorded total pressure remained unchanged at around 5.4 MPa. The periodic small variation corresponded well with the room temperature changes day and night (Figure 8b). Afterward, samples were partitioned into slices and each part characterized both visually and by X-ray diffraction. The minerals found at both the bottom (injection side) and top end are listed in Table 3.

Figure 8.

Liquid pressure (injection), total pressure and flux evolution of the SVV experiment: (a) Time curve in log scale and (b) time curve in linear scale.

Table 3. Results of Mineral Phases Analysis
MineralChemical FormulaeExperimentalSimulated
BottomTopBottomTop
  1. a

    Analysis by X-ray diffraction and by simulation after 35 days' experiment. (√, detected; ×, not detected)

HaliteNaCl
ThenarditeNa2SO4××××
BloediteNa2Mg(SO4)2 × 4H2O××
MgSO4MgSO4××
KieseriteMgSO4 × H2O×××
StarkeyiteMgSO4 × 4H2O××
PentahydriteMgSO4 × 5H2O××
HexahydriteMgSO4 × 6H2O××××
EpsomiteMgSO4 × 7H2O××××

5.2. Geochemical Reactions

[25] The possible mineral/water interactions in the sample by percolation with saturated NaCl solution are briefly described in the equations (5)(13).

[26] SVV

equation image

[27] Kieserite

equation image

[28] Starkeyite

equation image

[29] Pentahydrite

equation image

[30] Hexahydrite

equation image

[31] Epsomite

equation image

[32] Halite

equation image

[33] Thenardite

equation image

[34] Bloedite

equation image

[35] The molar volume of each mineral is listed in Table 2. For the series of MgSO4 × mH2O, it is clear to see that the molar volume of each mineral increases with the number of the crystal water molecules per unit mass of mineral. The molar volume of epsomite is more than three times that of anhydrous MgSO4.

[36] With the intrusion of NaCl saturated solution, MgSO4 powder begins to hydrate. Thus, free water is removed from solution. MgSO4 is converted into minerals with a higher molar volume; in addition, halite precipitates. The integral volume of solid phases increases. Under constrained conditions, the porosity of the sample decreases and consequently, permeability decreases. Simultaneously, crystallization pressure increases when the pore space is reduced to a small amount, which represents the total and residual pressure measured as shown in Figure 8b.

5.3. Batch Reaction Simulation

[37] To better understand the geochemical processes mentioned above, a geochemical-batch-reaction simulation was undertaken. In this modeling, saturated NaCl solution was gradually added to 8 mol anhydrous MgSO4 powder. The simulated results with ChemApp are shown in Figure 9. Initially, MgSO4 was present only. With the addition of saturated NaCl solution, MgSO4 was hydrated into kieserite (MgSO4 × H2O), and halite precipitated. The total volume of the solid phases increased. After the added H2O amounted to 8 mol, MgSO4was totally transformed into kieserite. By further adding solution, kieserite was hydrated into pentahydrite (MgSO4 × 5H2O). When the added H2O amounted to 40 mol, the concentration of pentahydrite reached the highest level. Thereafter, it began to hydrate into epsomite (MgSO4 × 7H2O). The maximum amount of epsomite was 8 mol after adding 56 mol of H2O. This corresponds to 8 mol of MgSO4 having reacted with 7 mol of H2O each. It is important to note that there was no aqueous solution left until then. All H2O in the adding solution was built into the crystals. With the further addition of NaCl solution, part of the epsomite and halite dissolved, while bloedite precipitated (Figure 9). The total volume of all solids decreased. Free water as well as aqueous solution began to accumulate.

Figure 9.

Simulated evolution of solid phase volume, where 8 mol of anhydrous MgSO4 is titrated with 1.5 kg water (equalling 83.26 mol) saturated with NaCl at 298.15 K and 100,000 Pa. The shown pattern is valid under the assumption of ideal mixing.

[38] It is important to note, that this simulation is ideal in the sense that at any point ideal mixing of all components constituting the system is established. Thus, water molecules are uniformly distributed among all MgSO4 crystals. Gibbs energy minimization requires that as the total water content increases all possible hydrates are formed consecutively, depending on their Gibbs energy of formation. Only when the total amount of water molecules exceeds that of SVV by a factor of 7, free water can be left after the reaction. This situation is to be strictly distinguished from a real system in the experiment where aqueous, saturated solution infiltrates a porous medium, and where near the moving front of the solution local conditions may arise where higher hydrates are formed than could be expected from the water content of the system as a whole. This becomes evident from a comparison of Figure 9 with Table 3: As the solution enters the sample, locally enough free water is present to form a pentahydrate and tetrahydrate, even though the amount of water molecules in relation to the total mass of anhydrous MgSO4 would rather form a monohydrate.

5.4. Reactive Transport Simulation

5.4.1. Model Setup

[39] The 2-D axisymmetrical geometry and discretization was set up according to the sample size (Figure 10). Initially, there is only anhydrous MgSO4 without any aqueous solution. Free water as well as Na+ and Cl were transported from the bottom by advection and diffusion. The diffusion coefficients of all species were the same as 1.0 × 10−9 m2/s. The tortuosity was constant with 1.0. The injection pressure at the bottom was time dependent according to the recorded liquid pressure in Figure 8. Owing to the symmetrical properties of the problem, it is actually a 1-D problem; therefore, a 1-D profile along the vertical axis was selected to observe the vertical variations of different variables (e.g. ionic concentration, mineral concentration) with time.

Figure 10.

Geometry and model setup.

[40] The material properties of the sample were as follows: initial porosity was set as measured at 50.2%, the initial permeability in 3.02 × 10−10 m2 was calculated based on the porosity (n) – permeability (k) relationship (equation (14)), which was derived from systematic experimental data for crushed salt with similar properties [Zhang et al., 2007]. This relationship was also adopted for the simulation of the porosity-induced permeability change during the experiment.

equation image

[41] In order to avoid the zero or even negative porosity owing to the crystallization process, a minimum porosity was set to 0.0004, which corresponds to a value that matches the measured permeability of 1.62 × 10−26 m2 according to equation (14). To simulate the solution supply during the experiment, the time-dependent liquid pressure was applied to the bottom boundary as shown in Figure 11, which corresponds to the descriptions in section 5.1. At the beginning of the experiment, a liquid pressure of 10 Pa only was applied. After several hours, the maximum fluid pressure (3.5 MPa) was set. After about 2 days, the system was closed for 17 days, which means no solution could enter the sample. This was treated as a release of liquid pressure and set the liquid pressure to zero. In this stage, diffusion inside of and into the sample were the only transport mechanisms. After that, the injection system was switched on again for 1 week (the second injection) applying the same injection pressure (3.5 MPa). Little solution was injected into the sample. Therefore, the injection system was removed for the remaining experimental time.

Figure 11.

Time-dependent liquid pressure at the bottom.

5.4.2. Simulated Results

[42] Hydration, precipitation, and dissolution processes after the intrusion of saturated NaCl solution into the initially porous anhydrous MgSO4 rapidly changed the hydraulic properties of the sample. The simulated results of the simplified 2-D example are shown by a cross section along the vertical axis in Figures 1215. Initially, only anhydrous MgSO4 was present. Upon intrusion of NaCl saturated solution, anhydrous MgSO4 was hydrated into kieserite (MgSO4 × H2O), and later on into pentahydrite (MgSO4 × 5H2O). Initially, the sample exhibited a very high porosity of 50.2%. Therefore, after only 540 sec, the solution front had almost reached the top, neo-formed kieserite being distributed along the sample within a height of 0.12 m. The hydration of kieserite resulted in the decrease of free water in the solution and thus halite (NaCl) precipitated (Figure 12a). The hydration of pentahydrite needs more water and occurred only at the bottom, where the solution was supplied.

Figure 12.

Simulated results of mineral abundances at 5.4 × 102 sec (a) and at 1.1 × 103 sec (b).

[43] The porosity and permeability of the sample decreased with the intrusion of solution as shown in Figure 13. This is due to the slightly higher molar volume of kieserite than anhydrous MgSO4 (Table 2).

Figure 13.

Simulated results of the porosity and permeability evolution for the SVV experiment (a) porosity profiles and (b) permeability profiles.

[44] With the further intrusion of saturated NaCl solutions, the reactions described above continued. The amount of anhydrous MgSO4 decreased, while the amount of the other minerals halite, pentahydrite, and kieserite increased (Figure 12b). The peak of kieserite indicates the hydration of anhydrous MgSO4 by limited free water supply and turned into pentahydrite as soon as enough water was presented. The kieserite peak moved upward (to the top). After about 2 h (7.6 × 103sec), anhydrous MgSO4 totally disappeared (Figure 14a). Minerals with larger molar volume like pentahydrite largely appeared within 2 cm from the bottom of the sample, and the pore space reduced and permeability decreased continuously, which corresponded to the phenomena observed experimentally. Within 2 h from the beginning of the experiment, solution easily flowed into the sample. Thereafter, the sample became low-permeable and solution had to be pressurized into it (Figure 11). With the aid of the first injection phase, more solution was injected into the sample. The kieserite from the bottom side totally transformed into pentahydrite, epsomite, and bloedite, all of which have a larger molar volume then kieserite. The total volume of the solid phases increased and locally may have been above the total volume of the sample. Under constrained condition, this can numerically result in a negative porosity, which is not possible in reality. This is owing to the lack of considering the coupled mechanical effect on the chemical process. In such a case, a crystallization pressure builds up (Figure 8), which is, however, not considered in the current simulation. To cope with the porosity change and its coupling effect on the hydraulic process, the minimum and maximum porosity values of 0.0004 and 1.0 were applied, respectively. The total volume of all precipitated minerals was calculated and used for evaluating the porosity change. If the calculated porosity was lower than the limited value, it was then cut to the limited value. By the end of the first injection phase (around 2 days), the amount of kieserite decreased along the whole sample. In contrast, the amount of halite, pentahydrite, epsomite, and bloedite increased (Figure 14b). The porosity and permeability values within the first 4 cm from the bottom side reached the minimum limits (Figure 13).

Figure 14.

Simulated results of mineral abundances at (a) 7.6 × 103 sec and at (b) 1.6 × 105 sec.

[45] After the first injection phase, the sample was closed for 17 days, and it reacted with the remaining solution plus a small amount in the instrumentation, e.g., the filter. The sample was isolated from the solution tank. In the numerical simulation, the liquid pressure was set to 0 but the geochemical boundary condition remained, which implied that the sample contacted with free NaCl solution during the closed period. Part of the sample reacted with the boundary solution and dissolved. Therefore, the porosity at the front in the sample remained unchanged, but the porosity at the bottom increased during the closed period (compare the curves at 1.6 × 105 sec ∼ 2 days, and at 8.51 × 105 sec ∼ 10 days in Figure 13a). Visual inspection of the disassembled sample after the experiment disclosed areas at the injection point where SVV had dissolved. The mineral distribution along the sample is shown in Figure 15a and 15b for the time before and after the second injection. The changes were very small which well matched the experiment with little solution injection.

Figure 15.

Simulated results of mineral abundances at (a) 1.72 × 106 sec and at (b) 2.35 × 106 sec.

6. Discussion

6.1. Mineral Composition

[46] At the end of the simulation (after 35 days), the mineral phases at the bottom and the top were compared with the experimental data (Table 3). The calculated occurrence of halite, thenardite, bloedite, hexahydrite, and epsomite was consistent with the experimental data. However, the hydrates MgSO4 × mH2O (m = 0, 1, 4, 5) differed from the experimental results. Theoretically, if anhydrous MgSO4 is reacted with free water, it turns into a hydrated form, depending on the activity of the water. In the experiment, there was anhydrous MgSO4 at both ends, which indicates that the sample was not entirely saturated with the solution. In other words, preferential flow existed during the percolation process. Therefore, locally there was enough water to form minerals with 4 or 5 H2O molecules. In the simulation it was assumed that the material and flow are homogenous. Therefore, anhydrous MgSO4 was transformed stepwise into kieserite, pentahydrite, and epsomite.

[47] During simulation, at the injection side, where the anhydrous MgSO4 contacted with saturated NaCl solution, kieserite formed first and later on pentahydrite and epsomite, resulting in a porosity decrease. After about 2 days, part of the MgSO4 hydrates began to dissolve and form bloedite, which resulted in the porosity increase. These processes can provide the explanation of the observed dissolution at the injection point of the sample after the experiment.

[48] Local conditions may have favored the formation of phases which were not expected theoretically, as can be deduced from the following reasoning. Nonuniform advection and diffusion of aqueous solutions in the sample does have an impact on the solid phase composition, as becomes evident from the results in Table 3. As the solution enters the sample, locally, enough free water is present to form pentahydrate and tetrahydrate even though the amount of water molecules in relation to the total mass of anhydrous MgSO4 would rather form monohydrate. As to pentahydrite and starkeyite, doubts exist as to whether or not these phases are thermodynamically stable at all because the naturally occurring MgSO4 hydrates are only kieserite, hexahydrite, and epsomite [Vaniman et al., 2004; Grevel and Majzlan, 2009]. But even if pentahydrite and starkeyite were considered metastable, and thus be suppressed in our calculation, hexahydrite would form instead of epsomite. Thus, on purely thermodynamic grounds, the system just does not contain enough water to form epsomite, but should contain hexahydrite. It is therefore hypothesized that the occurrence of pentahydrite and starkeyite in the experiment reflects nonhomogenous saturation of the sample in conjunction with local conditions as well as heterogeneity which prevents the hydration of hexahydrite.

6.2. Mineral Precipitation and Porosity Calculation

[49] In a normal soil system, precipitation and dissolution processes do not affect permeability to an extent that the resulting change in porosity has to be considered. However, in the current system, a large amount of volume change might occur, which can result in the situation that the total volume of the solid minerals exceeds the initial volume of the soil. Under a free-swelling condition, this is possible. However, if deformation is constrained, the pore space might be not enough for containing the whole amount of minerals that could form. Parts of such minerals were forced to remain dissolved in the solution. The solution will be oversaturated and result in crystallization pressure as measured in the experiment. This indicates a strong chemo-hydro-mechanical coupling effect, which will be considered in future work.

7. Conclusion

[50] A new reactive transport model based on the Gibbs energy minimization (GEM) approach was developed by coupling the commercialized thermodynamic simulator ChemApp to the OOP FEM simulator OpenGeoSys, which has the potential to simulate the nonisothermal multicomponent reactive transport under high concentration and high pressure in saturated/unsaturated porous media.

[51] The advantage of this model lies in its capability of simulating geochemical processes with little or even no free water. Due to the background of ChemApp, which has its roots in metallurgy and is usually applied to industrial purposes, further advantages lie in a variety of ready-to-use solid solution models, the modeling of nonadiabatic systems, and application to systems involving a nonideal gas phase. Therefore, the dynamic change of conditions in systems undergoing highly thermo-hydro-chemical processes can be accurately considered.

[52] This model was used to simulate a benchmark for reactive transport published in the literature and showed good agreement. This verified the coupling of flow and mass transport with the chemical reaction simulator. Further benchmarks for the calculation of geochemical reactions agreed well with the geochemical reaction code EQ3/6 and thus demonstrated that this model is capable of dealing with geochemical reactions in highly saline solutions as well as nonaqueous conditions. It indicates that the GEM approach is equivalent to the approaches based on the law of mass action as long as enough aqueous phases exist.

[53] The model was applied to simulate the chemo-hydraulic coupled processes in a laboratory experiment with anhydrous MgSO4 (SVV), in which there was no free water initially. With the intrusion of saturated NaCl solution, SVV reacted with free water. New solid phases, most of which contained hydration water, were formed. These phases exhibited a larger molar volume. The pore space and permeability were thus quickly reduced to a very small amount so that practically no solution could flow through the system even under an injection pressure of 3.5 MPa. Therefore, SVV is a potential sealing material for a HLW repository in a rock salt formation. The simulated results described the flow and geochemical phenomena observed in the experiment well.

Acknowledgments

[54] This work is funded by the German Ministry of Education and Research (BMBF) under grant 02C1295 and partially funded by 02C1638. Special thanks to the editor, Mavrik Zavarin and two anonymous reviewers for their valuable comments and suggestions. We thank Lothar Meyer (GRS) for the skillfully conducted experiments. Further thanks are extended to Peter Grathwohl (University of Tübingen), Sven Hagemann (GRS), Horst Juergen Herbert (GRS), Hua Shao (BGR), and Wenqing Wang (UFZ) for their support of this research work.

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